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مهندسی مکانیک و هوافضا - تبدیل فوریه در متلب
 
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پیوندهای روزانه
تبدیل فوریه در متلب

یک قضیه ریاضی می گوید که تقریبا همه توابع را می توان به عنوان مجموعه ای از دامنه های سینوسی و فرکانس های مختلف نشان داد. تبدیلات فوریه یک تکنیکی در ریاضیات است، که برای پیدا کردن دامنه ها و فرکانس های سینوسی آن می باشد. گسسته سازی تبدیلات فوریه –Discrete Fourier Transform  - (DFT) یک الگوریتم که محاسبات برای داده های عددی می باشد. تبدیل فوریه سریع یک  اجرا و پیاده سازی موثر و کارآمدی است. توبع زیر در متلب تبدیلات فوریه و عملیات مرتبط را انجام می دهد:

تبدیل فوریه سریع یک بعدی

fft

تبدیل فوریه سریع دو بعدی

fft2

تبدیل فوریه سریع چند بعدی

fftn

انتقال کندی (عقب افتادگی) صفر به مرکز تبدیل

fftshift

معکوس تبدیل فوریه سریع یک بعدی

ifft

معکوس تبدیل فوریه سریع دو بعدی

ifft2

معکوس تبدیل فوریه سریع چند بعدی

ifftn

قدر مطلق (اندازه اعداد مختلط)

abs

زاویه

angle

مرتب کردن اعداد مختلط بر اساس جفت های مزدوج مختلط

cplxpair

توان دو به بعد

nextpow2

زاویه فاز صحیح

unwarp

ادامه مطلب ...

دستور fft برای یک بردار ستونی:

>> y = [2 0 1 0 2 1 1 0]';

>> Y= fft (y)

 

Y =

 

   7.0000         

  -0.7071 + 0.7071i

   2.0000 - 1.0000i

   0.7071 + 0.7071i

   5.0000         

   0.7071 - 0.7071i

   2.0000 + 1.0000i

  -0.7071 - 0.7071i

اولین مقدار Y مجموع عناصر y است، و دامنه هایی که ازفرکانس های صفر یا ثابت هستند جزئی از سری فوریه هستند. عبارات 2 تا 4 (اعداد مختلط) دامنه هایی از فرکانس های مثبت مولفه های فوریه هستند. عبارت 5 دامنه ای از عنصر در فرکانس نایکوئیست، که نیمی از فرکانس نمونه برداری شده است. سه عبارت آخرمولفه های فرکانس های منفی هستند، که برای سیگنال های واقعی(real) ترکیبات اعداد مختلط از مولفه های فرکانس های مثبت هستند.

تابع fftshift  برای تنظیم یک تبدیل فوریه که در آن منفی و مثبت در دو طرف فرکانس صفر قرار می گیرد.

fftshift(Y)

 

ans =

 

   5.0000         

   0.7071 - 0.7071i

   2.0000 + 1.0000i

  -0.7071 - 0.7071i

   7.0000         

  -0.7071 + 0.7071i

   2.0000 - 1.0000i

   0.7071 + 0.7071i

و قدر مطلق Y برابر است با:

>> abs(Y)

 

ans =

 

    7.0000

    1.0000

    2.2361

    1.0000

    5.0000

    1.0000

    2.2361

    1.0000

معکوس سری فوریه Y را با تابع ifft بدست می آوریم:

>> ifft(Y)

 

ans =

 

    2.0000

   -0.0000

    1.0000

         0

    2.0000

    1.0000

    1.0000

         0

 

>> y

 

y =

 

     2

     0

     1

     0

     2

     1

     1

     0

 

 



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